EVENING DISCOURSES. 737 
of which were discovered by Mitscherlich in the year 1820, were for long believed 
to be exceptions, and until the year 1890 no actual evidence one way or the other 
was forthcoming. But it was eventually shown that the crystals of the members of 
an isomorphous series did differ, both in their angles and in all their other crystal- 
lographic and physical properties, although in the cases of the angles the differences 
were very small. Moreover, the differences were shown to obey a simple but 
very interesting law—namely, that they were functions of the atomic weight of 
the chemical elements of the same family group whose interchange gives rise to 
the series. [A series of lantern slides was next shown to illustrate this law.] 
All crystals possess one other obvious property, that of homogeneity, and we 
now know that it is the character of the homogeneous substance which determines 
the external form. There are no fewer than 230 different kinds of homogeneous 
structures, neither more nor less, the elucidation of which we owe to the inde- 
pendent recent labours of Schénflies, von Fedorow, and Barlow. And it is a 
significant fact that the whole of them fall naturally into the thirty-two classes of 
crystals, leaving no class unaccounted for. Of these 230 modes of regular repetition 
in space fourteen are the space-lattices long ago revealed to us by Bravais, and all 
recent investigation concurs in indicating two facts—first, thatlit is the space-lattice 
which determines the crystal system, and second, that it is the arrangement of 
the chemical molecules which is represented by the space-lattice. Each cell of 
the space-lattice corresponds to a molecule. The structure is certainly not solid 
throughout, however, part only being matter, and the rest ether-filled space, the 
relative proportions and the shape of the material portion being as yet unknown. 
We limit ourselves, therefore, to considering each molecule as a point, and we 
draw the lattice as a network of three systems of parallel lines, parallel to the 
directions of the three principal crystal edges, analogous, according to the system 
of symmetry, to those of the cube. The points of intersection we consider as those 
representing the molecules, inasmuch as any point within the limits of the cell 
may equally well be taken to represent the cell and the molecule, provided the 
choice is analogously made throughout the structure. [Such a space-lattice, one of 
the most general, triclinic, form, was shown on the screen. ] 
It has recently been found possible to determine the relative dimensions of 
these molecular cells, the distances of separation of the points of the space- 
lattice, in those cases where we know that the structure is similar, as in isomor- 
phous salts ; and the interesting discovery has been made that the ‘ molecular 
distance ratios,’ as these space-dimensions are called, are functions of the atomic 
weights of the interchangeable members of the family of chemical elements 
constituting the series, just as the crystal angles have been shown to be. 
We are now able, moreover, to take yet one further step, for the chemical 
molecules are composed of atoms, and it has been indubitably shown that the 
atoms occupy definite positions in the crystal. For when we replace, say, the 
alkali metal in a sulphate or selenate, by another, we observe a marked alteration 
in the crystal angles and the molecular distance ratio along a particular direction, 
this direction being the same whichever metals of the group are interchanged ; 
whereas if we replace the sulphur by selenium, a similar kind of alteration occurs, 
but along a totally different direction. Now we know that the atoms are arranged in 
the chemical molecule in what is known to chemists as their stereometric arrange- 
ment, depending on the maximum satisfaction of their chemical affinities. Hence 
this important experimental fact of the occupation by the atoms of definite posi- 
tions in the crystal proves firstly the homogeneous similarity of arrangement of 
the molecules, and secondly explains why we have classes or subdivisions within the 
systems. For it is the arrangement of the atoms within the molecule which causes 
the variations of the degree of symmetry, within the limits prescribed by the 
system and space-lattice; in other words, which determines the class, 
Now obviously any one of the atomsin the molecule may be chosen to represent 
the latter, and the points thus chosen analogously throughout the structure 
will constitute the molecular space-lattice. Hence the whole structure may be 
considered as made up of as many interpenetrating similar space-lattices as there 
are atoms in the molecule. The crystal structure will thus be dependent on two 
factors, the space-lattice and the scheme of interpenetration of the space-lattices, 
the former dominating the style of architecture, the crystal system, and the latter 
1909. 3B 
